Question

A random sample of

forty dash eightforty-eight

​200-meter swims has a mean time of

3.062

minutes. The population standard deviation is

0.090

minutes. A

95

confidence interval for the population mean time is

(3.041,3.083).

Construct a

95

confidence interval for the population mean time using a population standard deviation of

0.04

minutes. Which confidence interval is​ wider? Explain.

Answer 1

Here

sample mean

population standard deviation

and sample size

a 95% confidence interval for the population mean time using a population standard deviation of 0.04

Width of the confidence interval

First confidence interval is wider as width of the confidence interval is proportional to population standard deviation.